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• ... Can you briefly explain what the last occurance represents. First occurance seems obvious, assuming it s the smallest w such that a tuple of with w can
Message 1 of 3 , May 29, 2006
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--- Tom <tom@...> wrote:
> The latest info has been posted.
>
> Current information shows the difference growing
> at a rate of one additional prime every increase
> of 267 in width when looked at as a linear best fit,
> but the growth rate is tending to be concave up.
>
> A plot of k(width)-pi(width) versus width is at
> www.opertech.com/primes/trophy.jpg
> were k(width) is the number of primes in a interval.
>
> A list of first occurances (width) is at
> www.opertech.com/primes/trophycase.html

Can you briefly explain what the 'last occurance' represents. First occurance
seems obvious, assuming it's the smallest w such that a tuple of with w can be
found where k(w)-pi(w) takes the stated value, k(w) being the count of slots in
the tuple. Is the last occurance simply the w such that all larger w have a
currently known tuple with the stated delta?

That graph has a wonderful hockey-stick shape. I can think of no heuristic
which would suggest that it either ought to be asymptotically linear, or
concave up. Convex up would, however, surprise me, but again I couldn't explain
why.

Phil

Phil

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